1.

The value of `a`for which `a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=1`has a real solution is`pi/2`(b) `-pi/2`(c) `2/pi`(d) `-2/pi`A. `(pi)/(2)`B. `-(pi)/(2)`C. `(2)/(pi)`D. `-(2)/(pi)`

Answer» Correct Answer - B
The given equation is `ax^(2) + sin^(-1) ((x -1)^(2)+1) + cos^(-1) ((x -1)^(2) + 1) = 0`
Now, `-1 le (x -1)^(2) + 1 le 1 rArr x = 1`
So, we have `a + (pi)/(2) = 0 " or " a = -(pi)/(2)`


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